This disclosure relates generally to the field of electrical conductivity measurements of formations made from within wellbores drilled through such formations. More specifically, the disclosure relates to processing multiaxial induction measurements to obtain real-time formation anisotropy and dip information.
Measuring formations properties of a formation from within a wellbore using some conventional 3D triaxial electromagnetic induction tools generally includes measuring 9 component apparent conductivity tensors (σm(i,j,k), j,k=1,2,3), at multiple distances between an electromagnetic transmitter and the respective receivers, represented by index i. FIG. 2A illustrates an example arrangement of transmitters and receivers, and shows as a vector the nine component apparent conductivity tensor for one distance (spacing). FIG. 2B shows an arrangement of a transmitter and one receiver on such a triaxial measurement. The typical receiver will include a main receiver and a compensating or “bucking” receiver to cancel effects of direct induction between the transmitter and the main receiver.
The measurements are usually obtained in the frequency domain by operating the transmitter with a continuous wave (CW) of one or more discrete frequencies to enhance the signal-to-noise ratio. However, measurements of the same information content could also be obtained and used from time domain signals through a Fourier decomposition process. This is a well known physics principle of frequency-time duality.
Formation properties, such as horizontal and vertical conductivities (σh, σv), relative dip angle (θ) and the dip azimuthal direction (Φ), as well as borehole/tool properties, such as mud conductivity (σmud), hole diameter (hd), tool eccentering distance (decc), tool eccentering azimuthal angle (ψ), all affect these conductivity tensors. FIG. 3A illustrates a top view, and FIG. 3B illustrates an oblique view of an eccentered multiaxial induction tool disposed in a borehole drilled through an anisotropic formation with a dip angle. Using a simplified model of layered anisotropic formation traversed obliquely by a borehole, the response of the conductivity tensors depends on the above 8 parameters (σh, σv, θ, Φ, σmud, hd, decc, ψ) in a very complicated manner. The effects of the borehole/tool to the measured conductivity tensors may be very big even in oil base mud (OBM) environment. Through an inversion technique, the above borehole/formation parameters can be calculated and the borehole effects can be removed from the measured conductivity tensor. In FIGS. 3A and 3B, X and Z are axes of the coordinate system fixed on the borehole, the Y axis is perpendicular to X an Z is in the direction into the paper (right-hand-rule) θ and Φ are the relative dip and dip azimuth of the formation, respectively, decc is the tool eccentering distance and ψ is the azimuth of eccentering.
After the borehole correction, the borehole corrected measurements may be further processed with a simplified model which does not contain a borehole. For example, one may use a simple model of uniform anisotropic formation with arbitrary dip angle with respect to the tool as illustrated in top view in FIG. 4A and in oblique view in FIG. 4B. The foregoing model can be called a zero-dimensional (ZD) model because the model formation does not have variation in the axial and radial direction of the tool. Example implementations of the ZD model are described in more detail in International Patent Application Publication No. WO2011/091216, the contents of which are hereby incorporated by reference in their entirely. In the ZD model, the controlling parameters are formation horizontal (Rh) and vertical (Rv) resistivities, the relative dip angle (θ) and the dip azimuth angle (Φ). In actual well logging conditions, the foregoing formation properties are generally unknown. Given the unknown parameters in such environment, the simple ZD model is actually the most versatile processing model to be used to generate coarse estimates of formation properties over the wellbore (borehole) path. These coarse Rh, Rv, dip, and azimuth values (presented with respect to depth, called a “log”) could be used to define zones where other higher order model inversion is applicable. For example, 1D inversion (e.g., Wang et al, “Triaxial Induction Logging, Theory, Modeling, Inversion, and Interpretation” SPE 103897, 2006, incorporated herein by reference) is appropriate to improve the vertical resolution of the Rh and Rv logs over a zone where Rh and Rv are varying but the dip and azimuth are almost constant.
Before multiaxial induction tools were invented, most of the induction tools only used axial coils or ZZ coils (coils with magnetic moment directed along the axial direction, or Z coordinate direction, of the tool) for the measurement. Such a ZZ coil tool could effectively measure only horizontal resistivity in a vertical well through horizontally layered formations, or any combination of well inclination and formation dip where the tool axis was perpendicular to the bedding planes). For many hydrocarbon bearing zones, the condition of vertical wells through horizontally layered formations is not common. The formations usually are characterized by Rh, Rv, dip, and azimuth of the layers. The apparent conductivity tensor measured by the triaxial induction tool is sensitive to the above formation parameters. Various inversion techniques, such as axial ZD and 1D inversion (e.g., Wang et al, “Triaxial Induction Logging, Theory, Modeling, Inversion, and Interpretation” SPE 103897, 2006, incorporated herein by reference), have been developed to solve for the formation parameters from the triaxial measurements. The axial 1D inversion model allows layered anisotropic formations to have different Rh and Rv values for each layer. However, the axial 1D inversion model requires the dip and azimuth of all the anisotropic layers within the processing window to be the same. If those assumed model conditions actually exist, the axial 1D inversion could produce higher resolution Rh and Rv logs in each layer than those from ZD inversion. The results are free from adjacent layer (“shoulder bed”) effects.
Under actual well logging condition, the dip and azimuth of the formations are generally not well known and may be highly variable. If one applies axial 1D inversion indiscriminately, there is no effective way to discern whether the axial 1D model assumptions are met or not. Therefore, the validity of the resultant logs becomes questionable.
Through extensive study using model data and real logs, it is apparent that the Rh, dip, and azimuth logs from ZD inversions have a reasonably good vertical response, while the Rv log is often distinctly has poorer vertical response compared with Rh, dip, and azimuth logs. Consequently, the ZD's Rv log often misses the true Rv value of thin beds of thickness of 1 to several feet.
More specifically, the logs from RADAR processing, e.g., conventional inversion processing, which is a mark of the assignee of the present invention, currently used in tools such as the RT SCANNER tool, which is also a mark belonging to the assignee of the present disclosure, and as described more fully in International Application Publication No. WO2011/091216, hereby incorporated by reference) or ZD processing show that most of the formations encountered in the oil field are 3D formations. Inversions using a 3D formation model are a method to obtain accurate logs in 3D formations. However, at this time, 3D inversion is still very time consuming and not practically available for oil field applications. The Rh, dip, and azimuth logs from RADAR processing or ZD processing generally have good vertical response in 3D formations because of the small radius of the influence sphere which is of order of the transmitter-to-receiver spacing. Due to the inherently lower sensitivity, the Rv log, however, shows distinctly poorer vertical resolution then the Rh, dip, and azimuth logs. Depending on the resistivity contrast between adjacent beds and the bed thicknesses, some significant shoulder bed effects may exist. These shoulder bed effects may cause the Rv logs from RADAR processing or ZD processing to incorrectly indicate resistivity of thin beds, particularly those of thickness from 1 ft to 5 ft. For beds thinner than 1 ft, the logs from RADAR processing or ZD processing may return values representing those of the bulk anisotropy properties of the thinly laminated formation. For beds thicker than 5 ft, such processing usually can resolve the correct bed resistivity value at the center of the bed. The lack of vertical resolution of the Rv log significantly limits the accuracy of the net hydrocarbon volume in place prediction over such thin beds.
Accordingly, there is a need in the art for methods and systems for obtaining and processing downhole conductivity measurements that overcome one or more of the deficiencies that exist with conventional methods.